Learning Objectives

1. Introduce the concepts of refrigerators and heat pumps and the measure of their performance.

2. Evaluate the maximum possible coefficient of performance for refrigerators and heat pumps based on the reversed Carnot cycle.

3. Analyze the ideal vapor-compression refrigeration cycle.4. Analyze the actual vapor-compression refrigeration cycle.

1 Refrigerators and Heat PumpsRefrigerator

• A device that transfers heat from a low-temperature region to a high-temperature region

• The objective of a refrigerator is to maintain the refrigerated space at a low temperature by removing heat from it

Refrigerant• The working fluid used in a refrigeration cycle

Heat Pump• Another device that transfers heat from a low-

temperature region to a high-temperature region

• The objective of a heat pump is to maintain a heated space at a high temperature

1 Refrigerators and Heat PumpsCoefficient of Performance (COP)

• A measure of performance for refrigerators and heat pumps

Tons of Refrigeration• One ton of refrigeration is equivalent to

211 kJ/min or 200 Btu/min

in net,R InputWork

Effect CoolingCOPW

QL

Input RequiredOutput DesiredCOP

in net,HP InputWork

Effect HeatingCOPW

QH

1COPCOP RHP

2 The Reversed Carnot CycleOverview

• The Carnot cycle consists of four totally reversible processes: two isothermal and two isentropic

• The Carnot cycle has the maximum thermal efficiency for a given maximum and minimum cycle temperature

• It serves as a standard against which actual cycles can be compared

• All four processes that comprise the Carnot cycle can be reversed• Reversing the direction of the processes also reverses the direction

of any heat and work interactions• The result is called the reversed Carnot cycle: a cycle that operates

in the counter-clockwise direction on a T-s diagram

2 The Reversed Carnot CycleCarnot Refrigerator or Carnot Heat Pump

• A refrigerator or heat pump that operates on a reversed Carnot cycle• The most efficient refrigeration cycle operating between two

specific temperature levels

• Consider a reversed Carnot cycle executed within the saturation dome of a refrigerant

2 The Reversed Carnot CycleCarnot Refrigerator or Carnot Heat Pump (cont.)

• The coefficients of performance are expressed in terms of the temperatures as

• In practice, the reversed Carnot cycle is not a suitable model for refrigeration cycles

• Processes 2→3 and 4→1 (isentropic processes) cannot be approximated closely in practice

• Process 2→3 involves the compression of a liquid-vapor mixture

• Process 4→1 involves the expansion of a high-moisture-content refrigerant through a turbine

11COP Carnot R,

LH TT

HL TT

11COP Carnot HP,

3 The Ideal Vapor-Compression CycleOverview

• Many of the impracticalities associated with the reversed Carnot cycle can be eliminated by vaporizing the refrigerant completely before it is compressed and by replacing the turbine with a throttling device, such as an expansion valve

• The cycle that results is called the ideal vapor-compression refrigeration cycle

3 The Ideal Vapor-Compression CycleIdeal Vapor-Compression Refrigeration Cycle

• The ideal vapor-compression refrigeration cycle consists of the following four processes

1→2 Isentropic compression in a compressor2→3 Constant pressure heat rejection in a condenser3→4 Throttling in an expansion device (irreversible)4→1 Constant pressure heat absorption in an evaporator

3 The Ideal Vapor-Compression CycleHousehold Refrigerator

• In a household refrigerator, the tubes in the freezer compartment where heat is absorbed by the refrigerant serve as the evaporator

• The coils behind the refrigerator, where heat is dissipated to the kitchen air, serve as the condenser

3 The Ideal Vapor-Compression CycleProcess Diagrams

• Recall that the area under the process curve on a T-s diagram represents the heat transfer for internally reversible processes

• The area under the process curve 4→1 represents the heat absorbed by the refrigerant in the evaporator

• The area under process curve 2→3 represents the heat rejected in the condenser

• Another diagram frequently used in the analysis of vapor-compression refrigeration cycles is the P-h diagram

• On this diagram, three of the four processes appear as straight lines

• The heat transfer in the condenser and the evaporator is proportional to the length of the corresponding process curve

3 The Ideal Vapor-Compression CycleThermodynamic Analysis

• All four components associated with the ideal vapor-compression refrigeration cycle are steady-flow devices

• The kinetic and potential energy changes of the refrigerant are usually small relative to the work and heat transfer terms and are therefore usually neglected

• The steady-flow energy balance on a unit-mass basis reduces to

• The condenser and evaporator do not involve any work, and the compressor can be approximated as adiabatic and isentropic

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3 The Ideal Vapor-Compression CycleCoefficient of Performance

• The COP’s of refrigerators and heat pumps operating on the vapor-compression refrigeration cycle can be expressed as

• The energy balance for the entire cycle givesLH qqww in comp,in net,

12

41

in net,RCOP

hhhh

wqL

12

32

in net,HPCOP

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wqH

4 Actual Vapor-Compression Refrigeration CyclesOverview

• Actual vapor-compression refrigeration cycles differ from ideal ones in several ways

• There are two common sources of irreversibilitiesFluid frictionHeat transfer to or from the surroundings

• The T-s diagram of an actual vapor-compression refrigeration cycle is shown below

4 Actual Vapor-Compression Refrigeration CyclesActual Refrigeration Cycles

• In practice, the refrigerant is usually superheated before entering the compressor

• The actual compression process involves frictional effects, which increase the entropy, as well as the heat transfer, which may increase or decrease the entropy, depending on the direction of the heat transfer

• The entropy of the refrigerant may increase (process 1→2) or decrease (process 1→2') during an actual compression process

• In actual cycles it is unavoidable to have some pressure drop in the condenser as well as in the lines connecting the condenser to the compressor and to the throttling valve

• The refrigerant is subcooled somewhat as it enters the throttling valve

Problem 1-1

A refrigerator uses refrigerant-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.12 and 0.7 MPa. The mass flow rate of the refrigerant is 0.05 kg/s. Show the cycle on a T-s diagram with respect to the saturation lines. Determine

(a) The rate of heat removal from the refrigerated space and the power input to the compressor

(b) The rate of heat rejection to the environment(c) The coefficient of performance

Problem 1-2

Refrigerant-134a enters the compressor of a refrigerator as superheated vapor at 0.14 MPa and –10 oC at a rate of 0.12 kg/s, and it leaves at 0.7 MPa and 50 oC. The refrigerant is cooled in the condenser to 24 oC and 0.65 MPa, and it is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, show the cycle on a T-s diagram with respect to the saturation lines, and determine

(a) The rate of heat removal from the refrigerated space and the power input to the compressor

(b) The isentropic efficiency of the compressor(c) The coefficient of performance of the refrigerator

Problem 1-3

A heat pump using refrigerant-134a heats a house by using underground water at 8 oC as the heat source. The house is losing heat at a rate of 60,000 kJ/h. The refrigerant enters the compressor at 280 kPa and 0 oC, and it leaves at 1 MPa and 60 oC. The refrigerant exits the condenser at 30 oC. Determine

(a) The power input to the heat pump(b) The rate of heat absorption from the water(c) The increase in electric power input if an electric resistance

heater is used instead of a heat pump